   # THE GAS LAWS

How do gases behave if their pressure, volume or temperature is changed. We can find this out by the following series of experiments.
It is sensible to vary two of the previous quantities while keeping the other constant in three separate experiments:
(i) Variation of pressure with volume at a constant temperature
(ii) Variation of pressure with temperature at a constant volume
(iii) Variation of volume with temperature at a constant pressure ## VARIATION OF PRESSURE WITH VOLUME

This can be investigated using the apparatus shown in the diagram. The air trapped in the glass tube is compressed by forcing in oil with the pump and taking readings of pressure and volume. After each compression you should wait a few moments to allow the temperature of the air to stabilise.

The relation between pressure and volume was first discovered by Robert Boyle in 1660 and is called Boyle's Law. It states that:

The pressure of a fixed mass of gas is inversely proportional to its volume as long as the temperature remains constant.

Pressure (P) = constant/volume(V) A graph of pressure against volume is shown in the following diagram for two different temperatures T1 and To (T1 >To). The lines on it are isothermals, that is they join points of equal temperature.

If a fixed mass of gas with a pressure P1 and a volume V1 changes at constant temperature to a pressure P2 and volume V2 Boyle's Law can be written as:

P1V1 = P2V2

(Remember that this equation applies only when the pressure and volume change isothermally – that is without any change in temperature – in other words at a constant temperature)

## VARIATION OF PRESSURE WITH TEMPERATURE This can be investigated using the simple apparatus shown in the diagram.

The water is heated and the pressure of the air in the sealed glass beaker is measured with the pressure gauge. (The volume of the air is effectively constant).

Results of this experiment show that for a fixed mass of gas at constant volume:

Pressure (P) = constant x absolute temperature (T)

If a fixed mass of gas with a pressure P1 and a temperature T1 changes to a pressure P2 and temperature T2 with no change of volume this can be written as:

Pressure law for a gas:    P1/T1= P2/T2

The variation of the pressure of the air with temperature is shown in the graphs below. Example problem
During a space walk an astronaut moves from the shadow of the spacecraft into full sun. The temperature of his oxygen tank rises from 200 K to 350 K. If the original pressure of the gas was 2 x105 Pa what is its new presure?

Final pressure (P2) = (2 x105x350)/200 = 3.5x105 Pa

## VARIATION OF VOLUME WITH TEMPERATURE This can be investigated using the apparatus shown in the diagram.
The capillary tube has a small plug of concentrated sulphuric acid placed in it and it is then sealed at the other end.

(It is most important that appropriate safety precautions are taken when carrying out this experiment. Your eyes must be protected.) The water in the beaker is heated and the length of the trapped air column and the temperature are both recorded.
Results of this experiment show that for a fixed mass of gas at constant pressure:

Volume(V) = constant x absolute temperature (T)

If a fixed mass of gas with a volume V1 and a temperature T1 changes to a volume V2 and temperature T2 with no change of volume this can be written:

Initial volume/Initial temperature = Final volume/Final temperature

or

V1/T1= V2/T2

This is known as Charles' Law.

Example problem
A cylinder of volume 4.0x10-3 m3 contains hydrogen at a pressure of 1.01 MPa. The gas is allowed to expand isothermally, that is without any change of temperature to a volume of 0.04 m3.

What is the new pressure of the gas?

P2 = (1.01x106 x 4 x10-3)/0.04 = 1.01x10-5 Pa